In a triangle ABC - N is a point on AC such that BN - AC- If BN 2- AN - NC- prove that - B -90-

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In a triangle...

Question

In a triangle ABC, N is a point on AC such that BN ⊥ AC. If BN² = AN . NC, prove that ∠B = 90°.

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Solution

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B N ⊥ A C

{B N}^{2} = A N \cdot N C

∠ B = 90.

∠ A B C = 90^{\circ}

∠ P C B = ∠ P B C

A B C

A B = A C

M

A B

N

A C

B M = C N

A M = A N

Δ A M C ≅ Δ A N B

B N = C M

Δ B M C ≅ Δ C N B

\times

A B C, A B = A C

D

A C

B C^{2} = A C \times C D

B D = B C

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